Hello, and thank you for your time.
I just started my A-levels derivatives/differentiation , and I would be more than happy if you could help me clarify it.
For example I know that y is a function in terms of x right?
y=f(x)
The derivative of it is f'(x)=dy/dx .
This means it is the rate of...
Hello,
I am working with the mass flow rate equation which is:
$$\frac{d \dot{m}}{dt}=\dot{m}_{in}-\dot{m}_{out}$$
To determine the change of the height of water in a reservoir. Assuming m_in = 10 and m_out = sqrt(20h), then :
$$\frac{d (\rho \cdot Q) }{dt}=\rho \cdot Q_{in} - \rho\cdot...
If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##.
Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial...
I am trying to create a function of A and x which has the following properties. A is a scaling parameter that determines the shape of the function. I write the function below in f(A,x) form
1) f(A,1)=1 always
2) For all x>1, 0<f ' (x)<1
3) As A approaches some upper bound (which could be...
Given the definition of the covariant basis (##Z_{i}##) as follows:
$$Z_{i} = \frac{\delta \textbf{R}}{\delta Z^{i}}$$
Then, the derivative of the covariant basis is as follows:
$$\frac{\delta Z_{i}}{\delta Z^{j}} = \frac{\delta^2 \textbf{R}}{\delta Z^{i} \delta Z^{j}}$$
Which is also equal...
Hi, friends! I read that, if ##f\in L^1[c,d]## is a Lebesgue summable function on ##[a,b]## and ##g:[a,b]\to[c,d]## is a differomorphism (would it be enough for ##g## to be invertible and such that ##g\in C^1[a,b]## and ##g^{-1}\in C^1[a,b]##, then...
Can someone help me with this?
(dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections).
A=pir^2
(dA/dt)=2pir(dR/dt)
Multiply through by (1/2pir)
(dA/dt)/(2pir)=dR/Dt
What is the rate of change of the radius for a circumfrance of 2
I just used the related rates formula that I derived for...
I can's understand the fact about the equation
i cant prove the equation from the first attachment to the second attachment pls help.
Sorry for bad english
I have a derivative of a function with respect to ##\log \left(r\right)##:
\begin{equation*}
\frac{dN\left(r\right)}{d \log\left(r\right)} = \frac{N}{\sqrt{2\pi} \log\left(\sigma\right)} \exp\left\{-\frac{\left[\log \left(r\right) - \log\left(r_M\right)\right]^2}{2...
Hi! As the title says, what is the derivative of a matrix transpose?
I am attempting to take the derivative of \dot{q} and \dot{p} with respect to p and q (on each one).
Any advice?
Hey there!
1. Homework Statement
I've been given the operators
a=\sqrt\frac{mw}{2\hbar}x+i\frac{p}{\sqrt{2m\hbar w}} and a^\dagger=\sqrt\frac{mw}{2\hbar}x-i\frac{p}{\sqrt{2m\hbar w}} without the constants and definition of the momentum operator:
a=x+\partial_x and a^\dagger=x-\partial_x with...
I am trying to explain to someone the formal notion of a limit of a function, however it has made me realise that I might have some faults in my own understanding. I will write down how I understand the subject and would very much appreciate if someone(s) can point out any...
1. Homework Statement
Trying to use change of variables to simplify the schrodinger equation. I'm clearly going wrong somewhere, but can't see where.
2. Homework Equations
Radial Schrodinger:
-((hbar)2)/2M * [(1/r)(rψ)'' - l(l+1)/(r^2) ψ] - α(hbar)c/r ψ = Eψ
3. The Attempt at a Solution...
So to find the x values of the stationary points on the curve:
f(x)=x3+3x2
you make f '(x)=0
so:
3x2+6x=0
x=0 or x=-2
Then to find which of these points are maximum or minimum you do f ''(0) and f ''(-2)
so:
6(0)+6=6
6(-2)+6=-6
so the maximum has an x value of -2 and the minimum has an x value...
1. Homework Statement
I know this is more of a physics question, but I tried there and wasn't successful.
I have done a physics experiment measuring the weight as a function time of the discharge of water from a cylindrical bottle with a pinhole at the bottom. What I ultimately want to get at...
C \in \mathbb{R}^{m \times n}, X \in \mathbb{R}^{m \times n}, W \in \mathbb{R}^{m \times k}, H \in \mathbb{R}^{n \times k}, S \in \mathbb{R}^{m \times m}, P \in \mathbb{R}^{n \times n}
##{S}## and ##{P}## are similarity matrices (symmetric).
##\lambda##, ##\alpha## and ##\beta## are...
Hi,
I'm writing a mathematical expression of energy distribution of a signal, and in the formula I’ve found first and second derivative of delta function. I have to analyze my result but couldn’t found how to read these two derivative from an energy point of view.
And how can we see further...
1. Homework Statement
Find the derivative of the function
y = (3-2x^3+x^6 )/x^9
2. Homework Equations
Derivatives
3. The Attempt at a Solution
I have tried to use the quotient rule
and got to
-6x^11 + 6x^14 - 27x^8 + 18x ^24 - 9x ^14 / (x^9)^2
Which doesn't look close to the answer...
1. Homework Statement
At time t, the position of a body moving along the s-axis is
s= t^3 -12t^2 + 36t m(meters)
Find the total distance traveled by the body from t = 0 to t = 3.
2. Homework Equations
Derivatives
3. The Attempt at a Solution
I got the derivative which is
3t^2 - 24t +...
Hey Guys!
I was working on an integration problem, and I "simplified" the integral to the following:
$$\int \limits_0^{2\pi} (7.625+.275 \cos(4x))^{1.5} \cdot (A \cos(Nx) + B \sin(Nx)) \cdot (Z-v \cos(x)) dx$$
This integral may seem impossible (I have almost lost all hope on doing this...
Since lnx is defined for positive x only shouldnt the derivative of lnx be 1/x, where x is positive. My books does not specify that x must be positive, so is lnx differentiable for all x?
I have been playing around with calculus for a while and I wondered what would it be like to make some changes to the definition of derivatives.
I'd like to look at the original definition of derivatives in this way (everything is in lim Δx→0):
F(x+Δx) - F(x) = F'(x) * Δx
The Δx factor...
A lot of web pages/books show how to use cosx=sin(Pi/2-x) and the chain rule to prove that the derivative of
cosx=-sinx. My question is how to use this identity and the defintion of the derivative to prove the same thing.
Or whether it is at all possible. Seeing that i get...
I can't figure out why my demonstration of snell's law fails, that's the demonstration: (I used a photo)
I think it fails because the function t (HO) represents a line and so the concept of minimum is not defined, when I take the derivative and equal it to 0 I'm considering the case when the...
1. Homework Statement
the original function is ##−6 x^3−3x−2 cosx##
##f′(x)=−2x^2−3+2sin(x)##
##−2x^2 ≤ 0## for all x
and ##−3+2 sin(x) ≤ −3+2 = −1##, for all x
⇒ f′(x) ≤ −1 < 0 for all x
3. The Attempt at a Solution
this problem is part of a larger problem which says
there is a...
1. Homework Statement
Find all stationary points of the function
G(x, y) = (x^3)*e^(−x^2−y^2)
2. Homework Equations
fx=0 and fy=0
3. The Attempt at a Solution
Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4)
Gx = 0 implies 3x^2-2x^4=0
x^2(3-2x^2)=0
hence x =0...
Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf
1. Homework Statement
As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...
I'm relatively new to calculus and I have a new chapter in my study which is on the Implicit Function, Implicit Differentiation and Higher Derivatives of a function, the problem is I don't understand the meaning of a 2nd or 3rd or whatever the higher derivative of a function is, what I know is...
After doing a couple courses in physics as well as calculus and differential equations, I was starting to wonder about splitting a derivate, such as ## \frac{dy}{dx} ##, into seperate pieces ##dy## and ##dx##. I know we've never done it in calculus or differential equations because it isn't...
1. Homework Statement
At 9 P.M. an oil tanker traveling west in the ocean at 18 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 8 P.M. while traveling north at 23 kilometers per hour. If the "spot" is represented by the origin, find the location of...